laws of biology, laws of nature: problems and (dis)solutions

Laws of Biology, Laws of Nature: Problems and(Dis)Solutions

Andrew HamiltonArizona State University

Abstract

This article serves as an introduction to the laws-of-biology debate.After introducingthe main issues in an introductory section, arguments for and against laws of biologyare canvassed in Section 2. In Section 3, the debate is placed in wider epistemologicalcontext by engaging a group of scholars who have shifted the focus away from thequestion of whether there are laws of biology and toward offering good accountsof explanation(s) in the biological sciences. Section 4 introduces two relatively newpieces of science – metabolic scaling theory and ecological stoichiometry – that have notbeen topics of much discussion by philosophers but are relevant because they have atleast some of the hallmarks of laws of nature. Section 5 concludes by pointing outthat discovering laws of biology, if any there be, will not necessarily answer the questionsraised by the debate in the first place: we will still want to know how biology comparesto other sciences, how to characterize its systems and processes, and whether accountsin terms of laws always usually constitute adequate explanations in various sciences.

1. Introduction

Laws of nature have been at the center of philosophical thinking aboutscience for several hundred years at least. In the last five decades, theselaws have been especially important in discussions of realism, explanation,determinism, causation, the quality of scientific inference and evidence,theory confirmation, the unity of science, scientific method, and the limitsof scientific knowledge. When philosophers offer positive accounts of howscience works, laws of nature often bear a great deal of the weight. Theascent of biology to premier status among the sciences in the second half ofthe twentieth century has moved philosophers and biologists to ask whetherthe focus on laws of nature is well placed. One important motivation behindthis question is that unlike the parts of physics that have long capturedphilosophers’ attention, biology has no generalizations or regularities thatcan uncontroversially be called laws of nature. In the absence of such laws,what are we to say about biology and biological knowledge? What are weto say about the scope of a philosophy of science that emphasizes laws of nature?

The literature contains several broad strategies for taking up thesequestions. One is to argue that there are strict laws of biology and thus that

© 2007 The AuthorJournal Compilation © 2007 Blackwell Publishing Ltd

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the issue of natural laws does not cause any special problems for law-basedphilosophy of science applied to biology. A second strategy is to argue thatthere are not and could not be laws of biology, but that there are laws ofphysics and chemistry. On the (very different) versions of this view thathave been articulated by Stephen Jay Gould, Alexander Rosenberg, andErnst Mayr (What Makes Biology Unique?), biology’s lack of laws is taken asstrong evidence that physics and biology are importantly different in methodor in the strength of their conclusions or in the kind of questionsposed. Arguments for and against laws of biology and what they might meanfor philosophy of science are surveyed in the next section below.

In recent years, there has been a parallel but connected discussion aboutthe biological sciences, resulting in what can be called a third strategy forthinking about the ways biology and laws of nature intersect in thephilosophical literature. In this discussion, biology, rather than laws, is takento be of primary interest, so the questions shift somewhat. Instead of askingwhat it means for biology and philosophy that clear cases of biological lawsare hard to come by, some have begun to ask what it means for laws that arigorous, productive, and theoretically rich science seems to operate withrelative paucity of strict empirical laws. This approach considers laws withina wider context of explanation as well as in a more local context of howparticular sub-fields of biology work – how they model phenomena, whatquestions are asked, how experiments are conducted, what counts as goodevidence, what the theoretical commitments are, and so on. In so doing,the question of whether there are laws of biology or not becomes secondaryto giving scientifically well-informed philosophical accounts of how particularkinds of explanation proceed and what kinds of features are characteristicof the systems of interest.

In addition to past and current conversations in philosophy about laws ofbiology and their importance in biological explanation, there are a coupleof recent developments in the biological sciences that are worth notingbecause they give an indication of what the future of the laws-of-biologydebate might hold. With one or two exceptions, philosophers have not yetgiven much attention to the large-scale integrative efforts now underwayin describing and understanding allometric scaling (West et al.; West andBrown) or to the application of stoichiometric thinking to community- andecosystem-level phenomena (Sterner and Elser). Section 4, below,contains a discussion of this work and places it in the context of the presentdiscussion.

2. For and Against Laws of Biology

Many of the arguments in favor of laws of biology proceed by attemptingto show that some particular biological generalization is a law, where ‘law’is understood in the sense that is usually associated with the logical empiricistmovement. That is, laws are universal, true, exceptionless, and ‘naturally’,

© 2007 The Author Philosophy Compass 2/3 (2007): 592–610, 10.1111/j.1747-9991.2007.00087.xJournal Compilation © 2007 Blackwell Publishing Ltd

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‘nomically’, or ‘empirically’ necessary, but not logically necessary.1 So, forinstance, Elgin argues that the scaling ‘laws’ that relate body mass to certainbiological processes are genuine laws of biology (Damuth; West, Brown,and Enquist). Ruse argues that the Hardy-Weinberg ‘law’ that describesallele distributions over successive generations of certain types of biologicalpopulations is a genuine law, and Ghiselin argues that Mayr’s ‘law’, whichsays that in certain circumstances, speciation cannot occur when the relevantpopulations of organisms are not geographically isolated from one another,is a law properly so called.

2.1. OBJECTIONS: ANTECEDENTS, UNIVERSALITY, AND HETEROGENEITY

As a more detailed example of this strategy, consider the following argumentdrawn from Elliot Sober (Philosophy of Biology). In the first three decades ofthe 20th century, Ronald Fisher was instrumental in the forging of thesynthesis between genetics and Darwinian theory and in the attendant birthof population genetics, the branch of biology that studies changes in genefrequency over time. One of Fisher’s lasting contributions is an explanationin terms of natural selection of the roughly equal distribution of males andfemales observed in many populations. Fisher showed by way of an elegantmathematical model that under certain conditions – random mating, heritablevariation of offspring sex distribution in the population of parent pairs, andso on – we should expect a 1:1 ratio of males to females. The argument,very roughly, is that for a given generation, call it F1, the number ofgrandoffspring, F3, is maximized by a 1:1 sex ratio in the F2 generation.Fisher’s model shows that there is no parental ‘investment strategy’ that hasa better payoff in terms of fitness (expected number of offspring) than theequal distribution unless there is already a bias in the population. Where thesex distribution is biased one way or the other, the best strategy formaximizing the size of the F3 generation is to produce more of whicheversex is less well represented in the population, moving the ratio toward 1:1.

According to Sober, the formalism developed by Fisher renders a law ofbiology properly so called. This law is as good and universal as any other,even if it turns out be instantiated only on Earth.2 Sober comes to thisconclusion partly by emphasizing the counterfactual force of laws: they don’tnecessarily tell us what is happening, they tell us what would happen werecertain conditions to obtain. If we construe laws as true universalgeneralizations of the general form ‘For all x, if x then y’, and we allow theconditions for application to be built into the antecedent – in this case wewill have a compound ‘x’ that articulates Fisher’s assumptions – then wehave a legitimate law. Whenever and wherever the antecedent conditionsobtain, Sober argues, a 1:1 sex ratio will follow, and it isn’t really relevantto the discussion of lawhood that the instances of the law holding are limited,as far as we know, to Earth. The law is universal in the sense that anywherethe relevant conditions obtain, a 1:1 sex ratio will follow.

594 . Laws of Biology, Laws of Nature


Arguments in favor of strict laws of biology have not been widelyconvincing. Standard objections are that there are serious concerns aboutwhat kind of latitude should be taken with building assumptions into theantecedents of laws, that biological laws lack the necessity and universalitythat are associated with the logical empiricists’ notion of laws of nature, andthat the biological sciences pay attention to variation among individuals inways that make law formation about biological systems or objects difficultor impossible. These objections are not always separate, as we will see shortly:necessity, universality, and individual variation all bear on the question ofwhat can rightly be included or excluded from the antecedents of law statements.

A driving thesis behind all these objections is that the systems under studyin biology are often taken to have what might be called ‘nomic inhibitors’(Hamilton, Laws, Causes, and Kinds). These are features of systems thatpreclude there being laws of those systems, or preclude our access to whateverlaws there may be. Nomic inhibitors are those features of systems that makeit the case that claims of universality or necessity fail. Many philosophersand scientists think that biological systems are nomically inhibited – complex,contingent, variable, and so on – in ways that the systems studied by physicistsare not, and that this is reason to think that there can be no laws of biology(Smart; Rosenberg; Mayr, Toward a New Philosophy of Biology).

Arguments from nomic inhibition bear directly on Sober’s argumentabout Fisher’s generalization. A basic concern with the argument is thatcomplex, variable, and contingent systems require so much to be packedinto the antecedents of putative law statements that the statements becomeunwieldy, only vacuously true, or both. Biology is not the only science forwhich nomic inhibitors are an issue, of course, and one way to object toSober’s defense of Fisher’s generalization in terms of its counterfactual forceis to point out that the putative sex-ratio law is just a special case of thelarger issue of whether building assumptions into the antecedents of universalconditionals can yield laws in any of the special sciences (Pietroski and Rey;Earman and Roberts).

To see the force of the objection about antecedents, consider again thesex-ratio case. With Fisher’s generalization, as with very many others acrossthe sciences, it isn’t quite accurate to say that whenever the initial conditionsspecified in the assumptions of the model are met, a particular outcome willfollow. This is because there are many confounding conditions that can,and often do, function to prevent the prescribed outcome. With sex ratiosthere are strong arguments that paternal care in birds and mammals play aconfounding role (Frank). There are also well-documented and much-discussed cases of female-biased ratios among arthropods that may be dueto group or kin selection (Hamilton; Wade; Sober, Philosophy of Biology).Other possible confounders for certain taxa of large mammals are overlappinggenerations, inheritance of maternal rank by daughters, and cooperationamong related mothers (see West, Shuker, and Sheldon for a review). Thisis, of course, only a partial list and there are other lists for other taxa.



There are also mechanistic confounders to consider: Fisher’s model isnormally understood to have been developed for populations in whichsex is determined by a single autosomal locus (Feldman, Christiansen, andOtto). Where sex is determined by multiple autosomal loci, the mechanismis different enough that deviations from equal distribution are expected(Lewontin and Kojima).

Confounding conditions like these have to be excluded for law statementsto be true. The problem with truth-saving qualifications can be formulatedas a dilemma. It is very unsatisfying and even ad hoc to say that a law holdsceteris paribus without saying precisely which other things must be equal.Doing so amounts to saying that laws hold except where they don’t. Withcomplicated, variable, or contingent systems, however, listing all the possibleexceptions can be impossible or can make for an intractably long list. Worsestill, listing all the exceptions runs the duals risks of (i) narrowing the scopeof the putative law so much that it loses some or all of its explanatory force,and of (ii) describing highly idealized situations that may not occur inanything like the real world. Are there any real-world situations, for instance,in which none of the possible confounders for some putative law of biologyare operating? If not, then the law statement is, strictly speaking, onlyvacuously true. So, either we have an ad hoc or incomplete law statement,or we have a law that derives its truth partly from its inapplicability to the world.

Concerns with the non-universality of putative biological laws are closelyrelated to those about antecedents and ceteris paribus clauses. In a well-knownsection of his Philosophy and Scientific Realism (1963), J. J. C. Smart puts theuniversality objection this way:

if the propositions of biology are made universal in scope, then such laws arevery likely not universally true. If they are not falsified by some queer species orphenomenon on Earth they are very likely falsified elsewhere in the universe. (54)

It is worth noting that the universality objection as Smart articulates itderives from deeper worries about nomic inhibition in biological systems;his concerns about the scope of biological generalizations are a result of hisunderstanding of biological systems themselves. The driving ideas are, asSmart goes on to argue, that putative biological laws cannot be universalbecause (i) biological objects and systems don’t have the kind of uniformitythat law statements describe, and (ii) that biological systems are not organizedsuch that the properties of more complex entities like organisms andecosystems can be reduced to those of the simpler entities that constitutethem. Here (i) can be understood as a claim about variation or non-homogeneity, while (ii) is about a particular kind of complexity.

Smart’s model science is physics, and he thinks that the stuff of physics isboth relatively simple (where ‘simple’ refers to a kind of hierarchicalorganization) and that its entities are more or less homogenous. On Smart’sview, an atom is an atom, and whatever complex features atoms have canbe explained by atomic theory, which makes reference to the electrons,protons, and neutrons that constitute them. This amounts to explaining



complex entities or their interactions at some macro level in terms of simpleentities and their interactions at a micro level. According to Smart,explanations that attempt such reductive explanations – those that proceedby accounting for the properties of a thing in terms of the properties of itsparts and their interactions – generally fail for biology.

These claims bear, of course, on the discussion above about specifyingantecedent conditions. Indeed, they serve as reasons to think that specifyingall the relevant qualifying clauses is a fool’s errand. Smart and many othersthink that it’s possible to discover strict laws in physics but not in biologybecause complex physical systems can be accounted for in simplerterms. Where such reductions are possible, the reasoning goes, the situationwith respect to ceteris paribus clauses is dramatically improved. Accountingfor atomic phenomena in terms of simpler parts makes for a shorter, lesscomplicated, and more widely applicable antecedent.

Homogeneity matters for very similar reasons. Zoologist and taxonomistErnst Mayr has recently reiterated what might be called the ‘variation’ or‘heterogeneity’ objection to laws of biology (What Makes Biology Unique?)that we saw in Smart a few paragraphs back and which Mayr himself hasbeen defending for nearly fifty years (‘Darwin and the Evolutionary Theory’).The argument, simply formulated, is that while the physicist can be happilyessentialist in her attitude toward her objects of study – an atom is an atomis an atom – the biologist does not have this luxury. Since variation is theraw material of natural selection and sometimes has fitness consequences,small differences between individuals in a population cannot be ignored.

The inanimate world consists of Plato’s classes, essences, and types, with themembers of each class being identical, and with the seeming variation being‘accidental’ and therefore irrelevant. In a biopopulation, by contrast, everyindividual is unique. (What Makes Biology Unique? 29)

If one’s view of laws is that they derive part of their explanatory powerfrom their universality – from their ability to say something true andnomically necessary about every instance of one kind of thing – then onewill be disconcerted by the kind of widespread variation for which Darwinargued. If we take Mayr at his word and countenance each biologicalindividual as unique, then laws are hopeless as explanatory devices becauseno law will be true of more than one individual. Not only would generalizingabout particular individuals be of dubious use in explanation, but it wouldnot result in laws, since a standard requirement of laws of nature is that theydo not mention individuals.

2.1. CONTINGENCY AND LAWLESSNESS

Turning now from concerns about the scope of biological generalizationsto whether they are more than accidentally true brings us to the secondstrategy for understanding laws of biology and their place in philosophy ofscience. On this view it is a mistake to look for laws of biology, because to© 2007 The Author Philosophy Compass 2/3 (2007): 592–610, 10.1111/j.1747-9991.2007.00087.xJournal Compilation © 2007 Blackwell Publishing Ltd


do so is an imposition: there just aren’t any lawlike regularities to be capturedin law statements. Biology is hopelessly and forever nomically inhibited, soa philosophy that requires laws of nature is wrongheaded. This approachmight be grounded in one or several arguments about nomic inhibitors.Ernst Mayr, for instance, has a version that is based partly on variation, aswe saw above. The most widely discussed approach, however, focuses oncontingency as a nomic inhibitor for biological systems.

An illuminating presentation of the contingency argument against lawsof biology is found in Wonderful Life (1989), where paleontologist StephenJay Gould offers the following thought experiment:

I call this experiment ‘replaying life’s tape’. You press the rewind button and,making sure you erase everything that actually happened, go back to any timeand place in the past . . . Then let the tape run again and see if the repetitionlooks at all like the original. . . . Any replay of the tape would lead evolutiondown a pathway radically different from the road actually taken. (48, 51)

For Gould, the particular history of life is only loosely constrained bylaws of physics and chemistry, and explaining it requires paying carefulattention to contingent facts rather than to what happens as a matter ofnomic necessity. He writes:

I am not speaking of randomness (for E had to arise, as a consequence of Athrough D), but of the central principle of all history – contingency . . . A historicalexplanation does not rest on direct deductions from laws of nature, but on anunpredictable sequence of antecedent states, where any major change in any stepof the sequence would have altered the final result. This final result is thereforedependent, contingent upon everything that came before – the unerasable anddetermining signature of all history. (283; emphasis in the original)

Gould’s metaphysical and epistemological arguments on this topic areencapsulated well in these two swatches of quoted text. The central notionsare that biological systems are contingent in nature – there is no necessityin the particular path life happens to take – and that we should, therefore,recognize that law-based accounts will be inadequate for explaining thehistory of life.

Gould’s arguments have been extended and given philosophical rigor byJohn Beatty in ‘The Evolutionary Contingency Thesis’ (1995). On Beatty’sview, biological regularities like the scaling laws and Mendel’s laws are allevolved regularities, and nothing in evolutionary theory tells us that theycould not be other than they are. That is, they do not have the kind of naturalnecessity usually required of laws because they might well have beendifferent. This is partly because evolution’s fitness demands are not so specificas to dictate unique phenotypic arrangements, and partly because the variationsupon which selection operates are themselves random, at least with respectto fitness. Variations do not arise with a view toward increasing fitness.

For many environmental changes that precipitate changes in relativefitness, there will be several possible changes in phenotype that raise or



maintain fitness levels. Where the ability to regulate temperature is important,for instance, we find behavioral adaptations, changes in body size, and theevolution of feathers and fur. Given all this, it might also be the case thateven the most lawlike biological regularities will change: if the independentassortment of alleles at gamete formation that is described by Mendel’s secondlaw becomes less fit than an arrangement on which allele assortment is notindependent, then we might expect biased segregation to become prevalentand independent assortment to become rare or non-existent.3

While some of these arguments are compelling, none have been convincingenough to bring consensus to the question of whether there are laws of biology.The literature contains point-by-point responses (Ruse; Sober,‘Two Outbreaksof Lawlessness’; Elgin;Vermeij) to these objections that I will not canvashere. One reason, perhaps, that no consensus has arisen is that the evaluationof the examples offered by proponents of biological laws turns on so manyother kinds of knowledge and on one’s other theoretical commitments. Thatis, much depends on how one reads the examples of putative laws and on howmuch weight one places on whatever exceptions they may have. Is the fact thatthe gene-protein map is only nearly universal a reason to deny that generaliza-tions that rely on it are strict laws? Does the fact that Mendel’s law ofsegregation has gene-linkage driven exceptions mean that it is not a law,despite its holding widely across many taxa? Several of the standing disagree-ments about whether certain premises in these arguments should be acceptedor rejected have to do with differences in the epistemological or metaphysicalviews of the interlocutors. These commitments are not always made explicit.

3. Solutions and Dissolutions: Epistemology and Explanation

Against the backdrop of this discussion, several philosophers lately haveargued that answering the question of whether there are strict laws of biologydoes not much matter for the project they are most interested in, becausethe law-based framework for thinking about science does not seem to capturemost biological theory or practice well, even if biology does turn out tohave strict laws. Many of these thinkers take their impetus from a growingskepticism in general philosophy of science about laws of nature – includinglaws of physics – and the explanatory value of laws (Cartwright, How theLaws of Physics Lie; Dappled World; Giere, Explaining Science; Science withoutLaws), as well as from careful attention to biology and its practice(Brandon). There are now several solutions and dissolutions of philosophyof biology’s law problem on offer from this set of perspectives. Four arepresented in broad terms here.

3.1. MITCHELL’S PRAGMATIC LAWS

Sandra Mitchell has been arguing since the mid-1990s that the logicalempiricist notion of laws maintains as false dichotomy between necessaryand accidental states of affairs. According to her, there are no empirical



regularities that happen by necessity, because even the regularities of physicsare the way they are as a matter of history (Biological Complexity). Whateverdifferences there are between the generalizations made in biology and thosemade in physics, then, are not best accounted for in terms of the regularitiesof physics being necessary while those of biology are accidental. Rather, sheargues, the differences between the generalizations are best accounted forin terms of the causal stability (and certain other features) of the regularitiesthey capture.

Stability, unlike necessity, admits of degrees. If Mitchell is right aboutthis much, it will follow that the logical empiricist notion of laws isinadequate for providing a metric for judging the strength of generalizationsin science. Building on the work of Robert Brandon, Mitchell’s advice isthat instead of accepting the ‘normative’ view of laws passed down fromthe mid-20th century, we should adopt a pragmatic view. Instead ofconcerning ourselves with laws, we should be looking for what she calls‘pragmatic laws’ – we should pay attention to the several ways thatgeneralizations are used in biology and other sciences (Mitchell, ‘PragmaticLaws’; Biological Complexity).

Assigning degree of stability and understanding how generalizations areused in the sciences asks for a local approach. In contrast to the kind ofarguments Smart offers, Mitchell’s program demands that researchers areprecise about the kind and causes of nomic inhibition they make claimsabout. Since several kinds of generalization have the pragmatic functionserved by laws in accounts of explanation, specifying how a certaingeneralization works in a particular field or subfield of science and indicatingthe degree to which the system it describes is stable or contingent is part ofthe philosopher’s job.

This requires a great deal of attention to the particulars of the theory inwhich the generalization is embedded, the kind of features of the system ofinterest has, and the tools by which the system is investigated. This is thesense in which Mitchell’s approach is local: she does not assume that everygood, explanatory generalization of biology (or any other science) has thesame pragmatic role, scope, or strength. The search for laws, then, will atbest reveal how explanations work in some part of science, but not necessarilyin every part.

3.2. WOODWARD’S ACCOUNT OF CAUSAL EXPLANATION

Like Mitchell, James Woodward argues in a series of articles (‘Explanation’;‘Law and Explanation’) and in his book Making Things Happen: A Theory ofCausal Explanation (2003) that the focus on laws in giving accounts ofscientific explanation is misguided. The central insight is that what one wantsfrom an explanation is not knowledge about what will happen everywhereand all the time, but rather about what causal relations hold (or would hold)under certain conditions when the system of interest is manipulated from



the outside in particular ways. On this view, we should not be concerned ifsome generalization is not universal or exceptionless, so long as we are ableto determine the range of conditions under which the generalization holds.

Woodward’s dissatisfaction with laws is that they do not always give usthe kind of information his account of explanation demands. For him, thetest for a good (causal) explanation involves intervening on the system tosee if it responds in the way the explanation – an equation or model –predicts it will. Not all laws are such that they can be pressed into this kindof service. Take, for instance, Woodward’s example of the principle thatno object can be accelerated to superluminal speed. This principle is a lawif any are, and yet it does not tell us how to intervene on the system to seewhether and how the variables in it are causally connected. There is noin-principle counterfactual test one could perform to test the principle’sexplanatory value.

Of course, not every explanation that is testable by way of an in-principlecounterfactual intervention is a good explanation. Like the logical empiricists,Woodward values scope, because it is a measure of explanatory power.Unlike the logical empiricists, and like Mitchell,Woodward argues that thenecessary-accidental dichotomy makes it seem as though there are just twokinds of explanation: either they capture regularities that hold as a matterof natural necessity and are therefore good explanations, or they captureregularities that hold accidentally and are therefore defective.

Woodward’s alternative suggestion is that explanatory power is measuredas the range of invariance – the set of conditions under which the explanationholds. In physics, he argues, many explanations that are captured in equationswill have a very high degree of invariance, while in biology the equationswill hold under a smaller range of conditions. This doesn’t mean that theexplanations in biology are faulty. On the contrary, it means that biologistshave done a good job showing precisely the conditions under which theregularities they describe can and cannot be expected to hold. In either case,it’s range of invariance, rather than laws of nature that really matter.

3.3. WINTHER’S FORMAL/COMPOSITIONAL DISTINCTION

Rasmus Winther has argued (Formal Biology; ‘Parts and Theories’) that thelaws/non-laws dichotomy is not a result of a differential distribution ofnomic inhibitors across the disciplines, but rather is due to different kindsor styles of investigation. Winther identifies two such styles, which he calls‘formal’ and ‘compositional’. Formal biology is characterized by a focus onlaws of nature that capture the relations between abstract properties ofbiological objects in a formal way. Formal biology looks a lot the traditionalphilosopher’s picture of physics, in that the methods and preferred outputsare roughly the same. Mathematical population genetics is an example.

Compositional biology, by contrast, does not emphasize necessary relationsbetween abstract properties. The focus instead is on the concrete causal,© 2007 The Author Philosophy Compass 2/3 (2007): 592–610, 10.1111/j.1747-9991.2007.00087.xJournal Compilation © 2007 Blackwell Publishing Ltd


mechanistic, structural, and functional relations between wholes and theirparts. Examples of subfields of biology in which the approach is composi-tional are physiology, developmental biology, and molecular genetics. Ratherthan writing laws, practitioners of compositional biology aim to articulatein various ways how the biological whole of interest is constituted by itsparts and their interactions. One example of this kind of investigativeapproach is now well-known in the philosophy of biology because of agrowing interest in mechanistic explanation (Bechtel and Richardson;Machamer, Darden, and Craver). Mechanistic explanation is, however, onlyone way to think about relations between parts and wholes, and Wintheroffers compelling arguments to the conclusion that these relations havegenerally been understudied in the philosophy of biology.

It should be noted for the present discussion about laws of biology thatWinther’s distinction has to do with which sets of tools are brought to bearwhen attempting to understand and explain phenomena. He argues thatsometimes the very same system is subject to both styles of investigation bydifferent groups of investigators. The question of whether or not there arelaws of biology, then, takes on a different cast than it had in Smart’s work,because the implication is that if one abstracts in the right way, one is likelyto find lawlike relations. These mathematically stated abstractions, however,will not tell investigators what they want to know if they are asking aftercausal mechanisms of certain sorts or concrete relations between wholes andtheir parts. Winther, then, has shifted the discussion away from nomicallyrelevant features of systems and toward the goals and methods used bydifferent groups of researchers as they investigate the world. This is not tosay that one uses a particular method no matter what the state of affairs inthe world. It is to say, rather, that the set of investigative tools one usesimportantly constrains the way one approaches the world.

3.4. HAMILTON’S PARITY THESIS

In his Laws, Causes, and Kinds (2005) and in a forthcoming critical reviewAndrew Hamilton has argued that the nomically relevant differences betweenthe physical sciences and the biological sciences have been overblown, partlyas a result of a tendency to think of sciences as uniform and monolithic.In contrast to what he takes to be the standard view on which classicalmechanics is understood to be characteristic of all of physics and evolutionarytheory is understood to be characteristic of all of biology, Hamilton arguesthat there is a great deal of variation within particular sciences: there arenomically challenged subfields in the physical sciences and nomicallywell-behaved subfields in the biological sciences. This is because the classicnomic inhibitors – complexity, contingency, and variation – do not respectdisciplinary boundaries, but turn up in various forms and to greater andlesser degrees in systems studied across the sciences. Putting this thesis anotherway, philosophy has been too kind to physics, and not kind enough to



biology, and this is because philosophers and scientists have been paintingwith too broad a brush.

Consider, as just one example of this line of thinking, Ernst Mayr’s claimsabout variation from section 2 above. He, like Smart, understands variationto be a biology-specific concern: there are no laws of biology becausebiologists cannot ignore variation among biological objects, and the scopeof biological generalizations is therefore severely limited. It is not the case,however, that biologists always pay attention to variation. Sometimesvariation can be safely ignored. Take, for instance, the way certain ecologiststhink about predator-prey relations. Standard predator-prey models are acase in which the models are unquestionably typological: there are predatorsand there is prey, and their interactions are often modeled using of a set ofpartial differential equations in which variation among the individuals is noteven represented.

This single example is meant to illustrate a kind of parity thesis about thepresence and absence of nomic inhibitors. The point of the example is notto show that variation is unimportant in biology, nor is it to argue for lawsof ecology, but rather to urge that the usual comparisons between biologyand physics are not fine-grained enough. Not paying attention to theimportant local differences within sciences leads to impoverished thinkingabout the similarities and differences across sciences. On this view, somefields of biology may turn out to have laws and some fields of physics mayturn out not to. It’s possible to show that important fields within physicsare shot through with complexity, contingency, and variation, just as it ispossible to show that important fields in biology are less nomicallyproblematic than Smart, Mayr, and a great many others seem to think(Hamilton, Laws, Causes, and Kinds). Whether or not some field of scientificinquiry has laws, then, turns out not to be terribly informative. If all this iscorrect, then when we want to give an account of how explanation worksin a particular field, we should look to the features of the system of interest,as well as how the system is conceptualized, tested, and modeled, ratherthan primarily asking after laws.

4. New Developments: From Molecules to Ecosystems with Allometry andStoichiometry

Biology in its modern form is a relatively young science. It is still possible– despite in-principle philosophical arguments about certain nomic inhibitorsbeing peculiar to biology in kind or in degree – that some enterprisingresearcher will come up with a law of biology. This section characterizestwo recent efforts to capture large-scale biological patterns using simple,general rules. These two cases are included here because the scientific resultsare fairly new and are not widely known to the philosophical community.

The case is the study of allometry, which has uncovered regular patternsacross the biological world. Allometry is the study of relations between



organism or system size and the structure and processes within the organismor system. Some of the best-known researchers in this field are self-consciously seeking universal laws of biology. Their efforts are describedand critically discussed in the next subsection below.

A second field of interest is the fairly recent application of stoichiometricmethods first to ecosystems and then to all of biology. Stoichiometry is thestudy of the relationships between chemical reactants and their products.Ecological stoichiometry studies the ways in which chemical and energeticconstraints are governed by the availability of key chemical elements in thesystem (Sterner and Elser). Biological stoichiometry extends these results byspecifying genetic mechanisms for the evolution of organisms within theseconstraints. While the main proponents of ecological and biologicalstoichiometry do not claim to be working toward laws of biology, they doaim at a broadly synthetic account of biological phenomena. Section 4.2examines ecological stoichiometry as it might bear on the laws-of-biologydebate.

4.1 ALLOMETRY: UNIVERSAL SCALING LAWS?

Theoretical physicist Geoffrey West and his colleagues, ecosystem ecologistJim Brown and plant ecologist Brian Enquist, are developing what theyhope are biological analogues to Newton’s laws: ‘underlying universal lawsof life that can be mathematized so that biology can be formulated as apredictive, quantitative science’ (West and Brown 36). Parts of biology, ofcourse, are predictive and quantitative, but West and colleagues seem to belooking for something much more fundamental than population genetics:they want ‘a general quantitative theory of biological phenomena’ (42).

Underlying this work is a phenomenon in need of explanation: it haslong been noticed that scaling of metabolic rates seems to vary according toa power ‘law’. That is, there is a relation between size or mass on the onehand and metabolic rate on the other. Kleiber observed, for instance, thatwhen plotted on a log/log graph, basal metabolic rates in birds and mammalsare well represented by a line with a slope of approximately 0.75. FollowingWest and colleagues ( West, Brown, and Enquist; West and Brown) thisrelation can be represented as Y = Y0M3/4, where Y is the metabolic rate, Mis the mass of the organism, and Y0 is an organism kind-specific constant.

West and colleagues’ main work has been to generalize this equation. Ifwe let Y stand for any number of observable biological phenomena (e.g.,metabolic rate, heart rate, radii of aortas and tree trunks, RNA concentration,life span, growth rate, etc.), we can raise M to some power that captures therelation between Y and M well. Moreover, that power is almost always amultiple of ¼. The claim, then, is that Y = Y0Mb, where b is a quarter power,may well be a law of biology. West, Brown, and Enquist examinedapproximately thirty scaling phenomena, and reported close matches topredictions in all cases for which good data existed.



As we saw above, laws of nature are generally thought to be more thanaccidentally true. To some degree, then, the degree to which quarter-powerscaling is a law of biology, or even a law of nature, depends on what drivesit as much as whether it turns out to issue good predictions. After all, thereis a very regular and predictable relationship between the degree to whicha car’s accelerator is depressed and the velocity of the car, particularly incontrolled circumstances, but nobody thinks the relationship is lawlike oreven explanatory (Haavelmo).

West and colleagues (West, Brown, and Enquist;West and Brown) arguethat quarter-power scaling is a result of constraints on the network propertiesof biological distribution systems as ‘optimized’ by natural selection. At base,theirs is an account in terms of efficiency, the need for space-filling networks(all parts of the organism are served by the network), and taxon- orclade-specific canalization of the basic working parts of the networks (e.g.,nerves, capillaries, and leaves). Other accounts of quarter-power scalingmake different ontological assumptions (Banavar, Martin, and Rinaldo;Darveau et al.), however, so it is not clear that the one offered by West andcoworkers is the correct one.

The underlying reasons for scaling phenomena are central to the discussionof whether there are scaling laws and if so, whether scaling phenomena arefundamentally biological. If scaling regularities are, as West and coworkerssometimes argue, partly a result of natural selection’s operation, then Gould’sand Beatty’s concerns about contingency will have to be answered:quarter-power scaling might be a result of early canalization of a set ofprocesses in the same way that the genotype-phenotype map is often takento be an accidental outcome that was canalized early and is rigorouslyconserved (Crick). If, on the other hand, scaling phenomena are regular inthe biological world because of some feature that is common to all complexsystems of networks, then the quarter-power scaling law might be a genuinelaw of nature, but not a law of biology. Physicist Jayanth Banavar and hiscoworkers have offered arguments along these lines. They maintain thatthree-quarter scaling is a feature of any efficient network in which flow iscentral and resource uptake is peripheral. If this is correct, there may benothing particularly biological about quarter-power scaling phenomena.

Despite explicit claims of universality (West and Brown), there are alsosome concerns about how widespread quarter-power scaling phenomenaare. In addition to the obvious concern that if the phenomenon is anevolutionary outcome it might be Earthbound, there are is another scopeproblem: it is not clear which of what West and Brown call ‘key biologicalprocesses’ should scale according to a quarter-power law. Not all allometricprocesses do, and the theory does not offer much advice about its applicationconditions. Finally, there are also important exceptions, such as thosereported by Reich et al. for respiration rates in several dozen plant species.

What these exceptions mean is still under debate in the science literature(see, for instance, Enquist et al.). Philosophers also, one assumes, will find



much to discuss here. Those who argue that universality and exception-lessness are not, or are not always, marks of good explanatory generalizationsin physics will find evidence for parity between subfields across sciences.Others who think that physics does meet stringent requirements may findevidence here for the view that there are not and cannot be proper laws ofbiology even when the biological world is treated at a high level ofabstraction. Still others might be convinced that there are laws of biologyafter all (Elgin).

4.2. BIOLOGICAL STOICHIOMETRY

Biological stoichiometry aims to integrate ecosystem ecology and evolu-tionary biology, two fields that have not historically shared deep connectionswith respect to their underlying theoretical frameworks (Elser), and thus toprovide a ‘biology of elements from molecules to the biosphere’ (Sternerand Elser) by attending to the chemical underpinnings of life and its variousprocesses. One result is the growth-rate hypothesis (GRH) of Elser,Dobberfuhl, MacKay, and Schampel. The GRH is an attempt to accountfor observed patterns in ratios of carbon (C) to phosphorous (P) and nitrogen(N) to phosphorous in living things. Put simply, low C:P and N:P ratiosare associated with high growth rates. The GRH explains this relationshipin biochemical terms by pointing out that higher growth rates should meanhigher ribosomal RNA (rRNA) production due to higher demand forprotein synthesis. rRNA is P-rich, but supplies of P are not infinite, whichmakes P availability an important limiting factor in organismal growth rates.

While the GRH is framed here in biochemical terms, it has importantecological and evolutionary implications. It was first articulated in the contextof explaining shifts in food-web structure and attendant changes in C:N:Pratios in freshwater ecology. The puzzle was partly about why C:N:P ratioschange with the dominant fish species. The answer is that changes in fishare often attended by changes in herbivorous zooplankton species, andthat these zooplankton vary substantially in their elemental compositions(Andersen and Hessen); they also cycle and sequester key elements indifferent ways and to different degrees (Sterner, Elser, and Hessen).

The evolutionary connection that broadens ecological stoichiometry intobiological stoichiometry lies in asking after the evolutionary mechanism forchanges and differences in development and growth rates across zooplanktonspecies. In 2000, Elser et al. argued that natural selection operates on variationin the rDNA genes that code for rRNA. If this is correct, then there is afairly direct, bi-directional connection between ecosystem ecology andnatural selection. This result may generalize. P-RNA-growth relationshave recently been shown to hold in varying ecosystems and across severaltaxa, including fruitflies, bats, and bacteria (Elser et al., ‘Growth Rate-Stoichiometry Couplings’; Weider et al.). The relation also may hold fortumor growth: fast-growing tumors seem to have high P demands.



Biological stoichiometry and the GRH are relevant to the discussion oflaws of biology because of their integrative nature, ready application to newsystems, and predictive successes (Elser and Hamilton), despite there notbeing explicit claims about stoichiometric laws of biology in the literature.Stoichiometric approaches, first to ecology (Sterner and Elser) and then tobiology more generally (Elser), have been shown to apply quite widely acrossthe biological world and to bridge disciplines in ways that make for simpleexplanations that are very general in nature. Biological stoichiometry is stilldeveloping, and is doing so in conjunction with the allometric researchdescribed above (Gillooly et al.). Those philosophers who take simplicityand generality to be important markers of laws may find something here toponder.

As stoichiometric work proceeds, there will be a great deal in it forphilosophers to pay attention to. It is not yet clear what scope biologicalstoichiometry will claim for its findings or whether its principles will takethe form of classic, quantitative laws of nature. At present, the GRH isusually given in argument form, but there is no prima facie reason why therelation between key elements and growth rates cannot be given in abstractand general form. Research that is successful in the ways described heremight renew an old discussion of whether laws only come in such a form.It is also not clear where to draw lines between what is biological and whatis not: will biological stoichiometry reveal physico-chemical constraints onevolutionary outcomes such that whatever laws there may be are not reallybiological in nature? Or, since it is surely the case that the P-RNA-growthrelation is itself evolved, does accounting for it drive us right back to Gould’sand Beatty’s discussion of evolutionarily contingent outcomes?

5. Conclusions

While there is not consensus on the laws-of-biology question, there ismovement on two fronts. The recent trend away from a preoccupation withlaws and toward accounting for the workings of good science in other termshas opened new avenues for philosophical work. The heterogeneity ofmethods and systems within particular sciences that informs the thinkingbehind most of the alternatives to logical-empiricist style thinking exploredin section 3 above points to the conclusion that producing a generalizationthat is both a law of nature and distinctively biological is not obviously aworthwhile goal all by itself. Having such a law would not justify adherenceto what Winther (Formal Biology) has called law-based explanations, becausewe would still want to know why such laws are, or seem to be, relativelyrare in biology, and whether such explanations go any distance towardcapturing the details of biological theory and practice. Partly because of theshift away from laws as primary, new thinking about explanation is emerging,and new cases for philosophical study are being described by philosopherswho are working in close contact with scientists.



These new cases are a second front, and one reason they are interestingis that they may turn out to provide stronger candidates for biological lawsthan those parts of biology that are standardly discussed in the philosophicalliterature. If the general stance characterized in section 3 is correct, thenfinding a ‘genuine’ law of biology will not answer the questions with whichthis article began, but it will change the debate from one about the existenceof laws of biology to one about what, if anything, the discovery of a law ofbiology means for the way we understand what biology is, how it works,and how it relates to other fields of knowledge.

Short Biography

Andrew Hamilton’s research focuses on the conceptual and theoreticalfoundations of the biological sciences, particularly evolutionary theory andsystematics, as well as on the relationships between science and publicpolicy. Two goals of this work are to use the tools of philosophy to clarifyideas and arguments with the hope of making progress in answering empiricalquestions about the evolution of social behavior and group cohesion ininsects and to bring careful thinking about science to discussions of valuesand policy in the classroom and in public forums. Hamilton’s writing hasappeared in Biology Theory, Public Library of Science: Biology, Philosophy ofScience, Ancient Philosophy, the Oxford Handbook of Analytic Philosophy, andPhilosophy of Science: Focal Issues. Before accepting his current appointmentin the School of Life Sciences at Arizona State University, Hamilton taughtin the Philosophy Department at the University of California at Davis. Heholds a Ph.D. in Philosophy and Science Studies from the University ofCalifornia, San Diego.

Notes

* Correspondence address: Arizona State University, School of Life Sciences, Mail Code 4501,Tempe,AZ 85287, USA. Email: [email protected].

1 There is a great deal of fuss over what nomic necessity comes to, but the basic idea is that lawsof nature can’t be accidental and they can’t be logically necessary – their necessity must be empiricalor, perhaps, metaphysical, in nature. For an overview see Cartwright et al.2 Sober (‘Two Outbreaks of Lawlessness’) argues that there are no empirical laws of biology, butthis need not distract us from his universality claims with respect to this example, nor from thediscussion that follows below about ceteris paribus clauses in antecedents of generalizations likeFisher’s.3 For a more recent and detailed analysis of Gould’s contingency claims and their implications,see Beatty, ‘Replaying Life’s Tape?’. Beatty does not deal directly with laws of biology there, buthis findings – especially with respect to empirical tests of Gould’s views – are relevant to the presentdiscussion.

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laws of biology, laws of nature: problems and (dis)solutions

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